WASHINGTON—Republican senators Marco Rubio and Bob Corker said they planned to support the GOP tax plan, bolstering the chances of passage as party leaders planned to release final details of the plan later Friday.

Mr. Rubio of Florida agreed to vote for the overhaul after Republicans agreed to a more generous tax credit for people with children.

Mr. Corker, who had been the only Republican senator to vote against a Senate tax bill, reversed after conversations this week with Senate Majority Leader Mitch McConnell (R., Ky.) and Sen. Pat Toomey (R., Pa.).

“I know every bill we consider is imperfect and the question becomes is our country better off with or without this piece of legislation,” Mr. Corker said in a statement. “I think we are better off with it. I realize this is a bet on our country’s enterprising spirit, and that is a bet I am willing to make.”

Republicans plan on final votes in the House and Senate and look likely to pass the bill and send it to President Donald Trump before Christmas.

Lawmakers agreed to make more of the child tax credit refundable, which refers to the amount of money taxpayers get back from the government even if they pay no income tax. Such filers would now be able to get $1,400 of the $2,000-per-child credit, said Rep. Kristi Noem (R., S.D.), one of the members of the House-Senate negotiating committee. That is up from $1,100 in the version that passed the Senate.

The agreement doesn’t make one change that Mr. Rubio had wanted: that the credit be refundable from the first dollar earned, which would make it more generous for very-low-income households. The Senate bill starts making the credit refundable against household income above $2,500.

A spokeswoman said Friday afternoon that Mr. Rubio will vote for the plan. In two tweets, the Florida Republican called the tax-credit changes “a solid step toward broader reforms which are both Pro-Growth and Pro-Worker” while saying there was “still much more to do” in coming years.

Lawmakers offset the cost of the change by reversing a decision to allow the child tax credit for 17-year-olds. The final bill, like current law, would make it available only for children under age 17. Republicans set themselves a $1.5 trillion cap on their tax cut, and exceeding that would prevent them from passing the bill without Democratic votes in the Senate.

Republicans were signing the House-Senate agreement Friday morning, which clears the path for full votes in both chambers. The bill won’t be publicly released until later Friday, and that will show the final tradeoffs Republicans made as well as details like the rates and bracket structure.

Broadly, the bill would cut taxes on corporations and pass-through businesses such as partnerships and S corporations, and it would lower the top rate on the highest-earning households. It would nearly double the standard deduction—taken by those filers that don’t itemize their returns—but repeal the personal exemption. The deductions for state and local taxes and mortgage interest would be limited. The bill is expected to double the estate-tax exemption, repeal the individual mandate to have health insurance and allow oil drilling in the Arctic National Wildlife Refuge.

The bill would also revamp the rules for taxing U.S. companies’ foreign income and allow faster writeoffs for business investments.

The bill is likely to add about $1 trillion to budget deficits over the next decade, even after accounting for economic growth.

Democrats have seized on independent analysis that the tax bill would benefit high-income households and corporations the most, noting that many of the individual tax cuts would be temporary but corporate reductions permanent. They also have complained that they have been shut out of the process in crafting the bill.

“They just did it in the back room and probably with their lobbyist friends,” House Minority Leader Nancy Pelosi (D., Calif.) said on Thursday.

Republicans say that the economic analysis doesn’t capture the effects of creating a more favorable business climate, and they argue that under the new tax system, companies would pay workers more and create new jobs. Republicans also say that future Congresses will extend the individual tax cuts, which under the legislation would expire after 2025.

“It’s going to provide the kind of middle-class tax relief that’s desperately needed right now,” said Sen. Rob Portman (R., Ohio). “It’s critically important for setting the stage for American leadership going into the future.”

Mr. Rubio, of Florida, who voted for the Senate bill, had been objecting to changes Republicans have discussed since then and complained about his party’s priorities. GOP leaders were willing to set a 21% corporate tax rate instead of 20%, and lower the top individual tax rate to 37%, without changing the child credit. The Senate rejected his attempt to set the corporate tax rate at 20.94% to increase refundability.

Ms. Noem said Mr. Rubio hadn’t personally told her he would now support the bill, but she thought the boost would be enough to get him on board. The refundable piece of the credit is important to families with very low income, who pay payroll taxes but often don’t owe income taxes.

“I believe that we’re in a good spot and we should be able to earn his support,” Ms. Noem said.

Mr. Rubio has said he would oppose the bill unless the portion that is refundable was “meaningfully higher” than the 55% in the Senate-passed version.

“We have not seen bill text, and until we see if the percentage of the refundable credit is significantly higher, then our position remains the same,” Olivia Perez-Cubas, a spokeswoman for Mr. Rubio, said Friday morning.

A spokesman for Sen. Mike Lee, a Utah Republican who along with Mr. Rubio had sought a more generous child tax credit, said their office hadn’t yet seen the text of the bill.

The current credit is $1,000 and it is largely refundable, though that is limited for very-low-income families. The doubled credit in the Senate bill is designed to offset the loss of exemptions for household dependents.

Republicans have 52 seats in the 100-member Senate, meaning that any three GOP senators can block the tax bill. Sens. Susan Collins of Maine and Jeff Flake of Arizona have also said they are undecided on the final version. GOP Sens. John McCain of Arizona and Thad Cochran of Mississippi are having health problems, raising concerns among Republicans about their availability for a final vote.

Corrections & Amplifications The photograph accompanying this article is of Sen. Marco Rubio on Nov. 16. An earlier version the captions incorrectly said it was this week.